IEEE Trans Image Process. 2017 Aug;26(8):3680-3695. doi: 10.1109/TIP.2017.2700719. Epub 2017 May 2.
This paper proposes a joint framework wherein lifting-based, separable, image-matched wavelets are estimated from compressively sensed images and are used for the reconstruction of the same. Matched wavelet can be easily designed if full image is available. Also compared with the standard wavelets as sparsifying bases, matched wavelet may provide better reconstruction results in compressive sensing (CS) application. Since in CS application, we have compressively sensed images instead of full images, existing methods of designing matched wavelets cannot be used. Thus, we propose a joint framework that estimates matched wavelets from compressively sensed images and also reconstructs full images. This paper has three significant contributions. First, a lifting-based, image-matched separable wavelet is designed from compressively sensed images and is also used to reconstruct the same. Second, a simple sensing matrix is employed to sample data at sub-Nyquist rate such that sensing and reconstruction time is reduced considerably. Third, a new multi-level L-Pyramid wavelet decomposition strategy is provided for separable wavelet implementation on images that leads to improved reconstruction performance. Compared with the CS-based reconstruction using standard wavelets with Gaussian sensing matrix and with existing wavelet decomposition strategy, the proposed methodology provides faster and better image reconstruction in CS application.
本文提出了一个联合框架，其中基于提升的、可分离的、与图像匹配的小波从压缩感知图像中估计，并用于重建相同的图像。如果有完整的图像，匹配的小波可以很容易地设计。此外，与作为稀疏基的标准小波相比，匹配的小波在压缩感知 (CS) 应用中可能提供更好的重建结果。由于在 CS 应用中，我们有压缩感知的图像而不是完整的图像，因此不能使用现有的设计匹配小波的方法。因此，我们提出了一个联合框架，从压缩感知图像中估计匹配的小波，并重建完整的图像。本文有三个重要贡献。首先，从压缩感知图像中设计了一种基于提升的、与图像匹配的可分离小波，并用于重建相同的图像。其次，使用简单的传感矩阵以低于奈奎斯特率的速率对数据进行采样，从而大大减少了传感和重建的时间。第三，为可分离小波在图像上的实现提供了一种新的多级 L-金字塔小波分解策略，从而提高了重建性能。与使用高斯传感矩阵和现有小波分解策略的基于 CS 的标准小波重建相比，所提出的方法在 CS 应用中提供了更快更好的图像重建。
